Does anybody know how to do transformations for variations of y=x^2 such as variations from the parent graph of y=x(x-2)(x+2)?

On other y=x^2 graphs you can do: y=(x-2)^2 to move the graph 2 to the right, etc... I was wondering, what is the general rule for movment and transformation of y=x(x-2)(x+2)?

Thanks

(math test tommorow, ahhgg, i put this a couple places, but didn't realize there was a designated urgent section. sorry, i'm new)

Apr 15th 2007, 08:23 PM

Jhevon

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Quote:

Originally Posted by rabidzebu

Does anybody know how to do transformations for variations of y=x^2 such as variations from the parent graph of y=x(x-2)(x+2)?

On other y=x^2 graphs you can do: y=(x-2)^2 to move the graph 2 to the right, etc... I was wondering, what is the general rule for movment and transformation of y=x(x-2)(x+2)?

Thanks

(math test tommorow, ahhgg, i put this a couple places, but didn't realize there was a designated urgent section. sorry, i'm new)

well, graphing y=x(x-2)(x+2) is not really done by transformations.

Looking at the formula, you notice y = 0 when x = 0, or x = 2 or x = -2, so these are your x-intercepts. so draw these lines on your graph, where they cut the x-axis is where y=x(x-2)(x+2) will cut the x-axis. then plug in numbers in the different intervals.

you will have the interval (-inf, -2) and (-2, 0) and (0, 2) and (2, inf). when you plug in an x in each interval, you will get a positive or negative number. if the number is positive, the graph is above the x-axis in that interval, if the number is negative, the graph is below the x-axis in that interval. so for

(-inf, -2) plug in x = -3 for example, you get y = -15 < 0, the graph is below the x-axis

(-2, 0) plug in x = -1 for example, you get y = 3 > 0, the graph is above the x-axis

(0, 2) plug in x = 1 for example, you get y = -3 < 0, the graph is below the x-axis

(2, inf) plug in x = 3 for example, you get y = 15 > 0, the graph is above the x-axis

now hopefully you know what shape the graph will have, when expanded you will get an x^3 graph, so you will have two turns, and one end going to + infinity and the other going to -infinity

The graph is below. you should study all the transformation rules in your text book. texts books usually have the rules in one highlighted section